Technology adoption, capital maintenance and the technological gap

We study optimal growth models à la Nelson and Phelps (1966) where labor resources can be allocated either to production, technology adoption or capital maintenance. We first characterize the balanced growth paths of a benchmark model without maintenance. Then we introduce the maintenance activity via the depreciation rate of capital. We characterize the optimal allocation of labor across the three activities. Though maintenance deepens the technological gap by diverting labor resources from adoption, we show that it generally increases the long run output level. Moreover we find that equilibrium maintenance and adoption efforts respond in opposite directions to policy or technology shocks. When a technological shock occurs, the reduction of the equilibrium technological gap is incompatible with welfare maximization. Finally, we find that the long term output response to policy shocks is slightly higher in the presence of maintenance